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Formulate All
Objective
Formulate
Minimize \sum_{l=1}^{L} \text{OpeningCost}_l \cdot Y_l + \sum_{l=1}^{L} \sum_{c=1}^{C} \text{TransportationCost}_{lc} \cdot X_{lc}
Confidence:
5/5
M
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n
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m
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z
e
∑
l
=
1
L
OpeningCost
l
⋅
Y
l
+
∑
l
=
1
L
∑
c
=
1
C
TransportationCost
l
c
⋅
X
l
c
Minimize \sum_{l=1}^{L} \text{OpeningCost}_l \cdot Y_l + \sum_{l=1}^{L} \sum_{c=1}^{C} \text{TransportationCost}_{lc} \cdot X_{lc}
M
inimi
ze
l
=
1
∑
L
OpeningCost
l
⋅
Y
l
+
l
=
1
∑
L
c
=
1
∑
C
TransportationCost
l
c
⋅
X
l
c
Constraints
Formulate
\sum_{c=1}^{C} CustomerDemand[c] \cdot X[l, c] \leq MaxCapacity[l] \cdot Y[l], \quad \forall l \in \{1, \ldots, L\}
Confidence:
5/5
∑
c
=
1
C
C
u
s
t
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m
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r
D
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m
a
n
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[
c
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⋅
X
[
l
,
c
]
≤
M
a
x
C
a
p
a
c
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t
y
[
l
]
⋅
Y
[
l
]
,
∀
l
∈
{
1
,
…
,
L
}
\sum_{c=1}^{C} CustomerDemand[c] \cdot X[l, c] \leq MaxCapacity[l] \cdot Y[l], \quad \forall l \in \{1, \ldots, L\}
c
=
1
∑
C
C
u
s
t
o
m
erDe
man
d
[
c
]
⋅
X
[
l
,
c
]
≤
M
a
x
C
a
p
a
c
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t
y
[
l
]
⋅
Y
[
l
]
,
∀
l
∈
{
1
,
…
,
L
}
Formulate
\sum_{l=1}^{L} X_{l,c} = CustomerDemand_{c}, \quad \forall c \in \{1,2,\ldots,C\}
Confidence:
5/5
∑
l
=
1
L
X
l
,
c
=
C
u
s
t
o
m
e
r
D
e
m
a
n
d
c
,
∀
c
∈
{
1
,
2
,
…
,
C
}
\sum_{l=1}^{L} X_{l,c} = CustomerDemand_{c}, \quad \forall c \in \{1,2,\ldots,C\}
l
=
1
∑
L
X
l
,
c
=
C
u
s
t
o
m
erDe
man
d
c
,
∀
c
∈
{
1
,
2
,
…
,
C
}
Formulate
\text{NumberOfFacilitiesOpened} = \sum_{l=1}^{L} Y_l
Confidence:
5/5
NumberOfFacilitiesOpened
=
∑
l
=
1
L
Y
l
\text{NumberOfFacilitiesOpened} = \sum_{l=1}^{L} Y_l
NumberOfFacilitiesOpened
=
l
=
1
∑
L
Y
l
Formulate
CustomerAssignments_{l,c} \in \mathbb{Z}^+, \forall l \in \{1, \ldots, L\}, \forall c \in \{1, \ldots, C\}
Confidence:
5/5
C
u
s
t
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m
e
r
A
s
s
i
g
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e
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t
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l
,
c
∈
Z
+
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∀
l
∈
{
1
,
…
,
L
}
,
∀
c
∈
{
1
,
…
,
C
}
CustomerAssignments_{l,c} \in \mathbb{Z}^+, \forall l \in \{1, \ldots, L\}, \forall c \in \{1, \ldots, C\}
C
u
s
t
o
m
er
A
ss
i
g
nm
e
n
t
s
l
,
c
∈
Z
+
,
∀
l
∈
{
1
,
…
,
L
}
,
∀
c
∈
{
1
,
…
,
C
}
Variables
Symbol
Shape
Definition
Domain
BINARY
INTEGER
CONTINUOUS
BINARY
INTEGER
CONTINUOUS
BINARY
INTEGER
CONTINUOUS
BINARY
INTEGER
CONTINUOUS
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